Anyway, in languages with i-mutation the change a→e is quite common. However, it's not so much the sound change but the actual underlying process that is important. Many languages can share the change a→e, but it's the reason why that is of interest.

Anyway, in languages with i-mutation the change a→e is quite common. However, it's not so much the sound change but the actual underlying process that is important. Many languages can share the change a→e, but it's the reason why that is of interest.

Well, i-mutation is caused by i/j in nearby (or same) syllables, causing a vowel to move further forward, i.e. to be fronted. The equivalent sound change for consonants would be palatalisation, as consonants themselves cannot be 'fronted' as such. This because i/j to varying degrees possess the qualities 'front' and 'palatal', which can colour nearby sounds.

Vowels change naturally across languages. They almost always change to a nearby vowel. So for most languages where [a] and [e] are neighbors (or close) in the distribution of vowel phonemes, this isn't an unusual change. In many cases this is just fronting of a low unrounded vowel. But in languages with many contrasts that would be less likely, or would involve many steps.

Freknu's answer points out that there can be instances of assimilation where [a+i] becomes [e] (either two vowels merging together, or long distance assimilation, along the lines of vowel harmony). Another example of this is in Arabic dialects where diphthongs [ai] and [au] become [e] and [o].

But another way that this can happen is in a chain shift, where vowels move around in one way or another. This is why the English letter A is actually an example: original [a] shifted to [e], along with various other changes during the Great Vowel Shift around 500 years ago in English.

As a general answer to your question, this is fairly common because [a] and [e] are fairly close in their articulation, but I don't think this is any more common than any other similar vowel change between close vowels.

There is no inherent restriction on which path a sound shifts, towards the front, towards the back, higher, lower, anything is possible. It all depends on the underlying phonological structures and processes.

As I mentioned earlier, it's not so much the sound change as the underlying process that is important. Can /e/ shift to /a/? Yes, but that's unimportant. WHY (if so) does /e/ shift to /a/, is what is important.

Then again, I am kind of generalising (a lot), but the underlying processes are important as sounds can change for many reasons, and it's important to distinguish between the underlying reasons.

To put it in a medical proverb: study the disease, not just the symptoms.

Actually answering "why" is all but impossible. But we can talk in more general terms than just [a] becoming [e]. We can look at how this relates to more general patterns. For example, is it the only change at that time? Was the [e] space previously unfilled? If we look at Arabic dialects that previously had just three vowels and now have five, we note that diphthongs are more articulatory work and then they (ai, au) settled into the mid vowel space (e, o). That's not entirely a "why" answer, but it's getting closer.

Another way of looking at what freknu said is that it's entirely irrelevant whether one particular vowel becomes another particular vowel. It might be a little interesting for people who like languages, but beyond that it's of absolutely no value to know the details. It is more interesting to know the FACT that a vowel changed to a different vowel. And it is also interesting to know which vowels most often become which other vowels. Generally, as I said, they're not too far off in the articulatory space and they may be open spaces (or might result in a push chain where what was there also moves somewhere else).

Another way to look at this would be to ask WHEN this happens (not WHY). Are there any typological patterns to that? This is a kind of fronting. It probably often occurs in cases of vowel harmony (see Turkish). Maybe other cases too. That tells us something about the interaction between sounds and how they're represented as mental categories (involving, for example, phonological features).

Actually answering "why" is all but impossible. But we can talk in more general terms than just [a] becoming [e]. We can look at how this relates to more general patterns. For example, is it the only change at that time? Was the [e] space previously unfilled? If we look at Arabic dialects that previously had just three vowels and now have five, we note that diphthongs are more articulatory work and then they (ai, au) settled into the mid vowel space (e, o). That's not entirely a "why" answer, but it's getting closer.

Well, that's kind of the "why" I was thinking about

/ai/ → /eː/ is monophthongisation of a (unstressed?) diphthong, causing compulsory lengthening and fronting of /a/. That is a "why", or perhaps "how" would be more appropriate

"Why" this then in turn happened is probably impossible to know, as you said.

Most stochastic models of diachronic phonology offer fairly compelling explanations of why changes happen. There's no one size fits all answer for *e->a, but (like freknu suggests) stress patterns are going to be a good first place to look for clues.

Can it predict change? If it can't predict change, then it can't actually answer why. It can get closer, and it can generalize, but solving the "why" question would be the single biggest leap in historical linguistics since it began with the discovery of Proto-Indo-European.

I'm guessing those models look at stability and distribution within a system and look at why things move to optimize it. But can they get us to actually being able to predict changes? If so, I'm very interested!